The ISC is rather more advanced than what Robert Morris wrote. Among other techniques, it uses the recently developed PSLQ integer relation finding algorithm to identify any root of a polynomial with degree <= 5 and reasonable height, or linear combinations of Pi, log(2), log(3), square roots, et cetera.
Interestingly, the ISC's job is made easier by the fact that numbers which come up in "real life" tend to have linear combinations of "similar" values. For example, Pi behaves like a logarithm, so linear combinations of Pi and (poly)logarithms tend to pop up, while Pi^2 tends to occur in combination with the product of two logarithms. As a result, the ISC is optimized to pass sets of "similar" inputs to the PSLQ algorithm, which makes finding relations much faster without missing anything interesting.
